## Probability and Statistics with Applications

Department:
MATH
Course Number:
3670
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every Semester

Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.

Prerequisites:

MATH 2401 or MATH 24X1 or MATH 2411 or MATH 2551 or MATH 2550 or MATH 2X51

Course Text:

Introduction to Probability and Statistics for Engineers and Scientists, 5th edition, by Sheldon M. Ross

Topic Outline:
• Probabilities of Events:
Random experiments, events, sets, and probabilities
Probabilities for equally likely outcomes, elementary counting
Independent events
Conditional probability, Bayes theorem
Applications
• Random Variables and Their Distributions:
Discrete random variables: Binomial, geometric, Poisson, multinomial
Continuous random variables: Exponential, normal, gamma, Weibull
Poisson process, waiting times
Applications
• Expected Values and Functions of Random Variables:
Expectations and variances of standard random variables
Expectations of functions of random variables
Chi-square as the square of a normal, sums of independent random variables and reproductive properties of standard distributions
Central limit theorem
Applications
• Descriptive Statistics:
Random samples: data collection and presentation
Sample statistics: mean, median, quantiles
• Statistical Estimation:
Point estimates and their properties
Probability distributions for estimator, the t and F distributions
Confidence intervals
• Hypothesis Testing:
Single sample tests, means, variances
Comparison of two populations, means and variances
Applications
• Simple Linear Regression and Correlation:
Fitting a regression line
Inferences on the regression
Predictions for future responses
Correlation
Applications